Determining relative positioning information

ABSTRACT

A signal detecting unit configured to be associated with a first vehicle includes one or more signal sensors and one or more processors and is configured to receive one or more signals from one or more signal sources is associated with a second vehicle. A set of time values is determined based on arrival times of the signal(s), and a set of distance expressions is generated. A set of distance equations is generated based on the set of time values and the set of distance expressions, and the set of distance equations is solved to determine one or more positions associated with the first vehicle or the one or more signal sources within a defined coordinate system.

TECHNICAL FIELD

This disclosure relates generally to determining relative positioninginformation using one or more signal sensors and one or more signalsources, and more particularly, to determining relative positioninginformation between vehicles.

BACKGROUND

Various object-detection systems and techniques exist. For example,Sound Navigation and Ranging (SONAR) is a technique that uses thepropagation of sound waves to navigate or to communicate with or detectobjects. SONAR may be used for acoustic location in both water and inthe air, but has generally been supplanted by Radio Detection andRanging (RADAR) for determining the range, speed, and so forth, ofobjects in the air. SONAR encompasses two primary types of ranging anddetection schemes including passive SONAR, which involves listening forthe sound made by vessels, and active SONAR, which involves emittingpulses of sounds and listening for echoes that are generated. WhileSONAR is a relatively inexpensive technology and is fairly accurate atshort range, SONAR offers a relatively poor resolution compared to RADARand other ranging technologies.

RADAR is an object detection system that makes use of radio waves todetermine the range, altitude, speed, and so forth of objects. RADARtechnology generally includes a transmitter that transmits pulses ofradio waves or microwaves that bounce off of objects in their path. Theobjects return a portion of the wave's energy to a dish or antennatypically located in proximity to the transmitter. RADAR is not capableof directly determining position information between objects (e.g., anangular relationship between objects), which instead must be inferredfrom the range determination and an angle of the antenna. RADAR is arelatively expensive technology that provides better accuracy at longerranges and better resolution than SONAR, for example.

Another sensing and ranging technology—Light Detection and Ranging(LIDAR)—is an optical remote sensing technology capable of measuring thedistance to, or other properties of, a target, by illuminating thetarget with a pulse of light in the ultraviolet, visible, or nearinfrared spectrum from a Light Amplification by Stimulated Emission ofRadiation (laser) source. LIDAR systems include both coherent andincoherent detection systems, each of which further encompasses twotypes of pulse models—micropulse and high energy systems. Micropulsesystems use considerably less energy in the laser and are typically“eye-safe.” High energy systems are more commonly employed in conductingatmospheric research. LIDAR sensors mounted on mobile platforms (e.g.,vehicles, satellites, etc.) require instrumentation to determine theabsolute position and orientation of the sensor. Such instrumentationgenerally includes a Global Positioning System (GPS) receiver and anInertial Measurement Unit (IMU). Similar to RADAR, LIDAR is only capableof determining a distance between objects; any determination of positioninformation between objects must be inferred indirectly. While LIDARgenerally offers better accuracy and higher resolution than otherranging technologies, such as SONAR and RADAR, LIDAR is alsoconsiderably more expensive to implement.

BRIEF DESCRIPTION OF THE FIGURES

Throughout the detailed description that follows, reference will be madeto the accompanying drawings, which form part of this disclosure. Theaccompanying drawings are not necessarily drawn to scale. A briefdescription of each drawing follows:

FIG. 1A is a schematic representation of an interaction between vehiclesemploying a system in accordance with an embodiment of the disclosure.

FIG. 1B is a schematic representation of an interaction between vehiclesemploying a system in accordance with an alternate embodiment of thedisclosure.

FIG. 1C is a block diagram that schematically depicts components of asystem in accordance with the embodiment of the disclosure depicted inFIG. 1A.

FIG. 1D is a block diagram that schematically depicts components of asystem in accordance with the embodiment of the disclosure depicted inFIG. 1B.

FIG. 1E is a schematic depiction of the transmission and receipt ofsignals in accordance with the embodiment of the disclosure depicted inFIGS. 1A and 1C.

FIG. 1F is a schematic depiction of the transmission and receipt of asignal in accordance with the embodiment of the disclosure depicted inFIGS. 1B and 1D.

FIG. 2 is a flow diagram illustrating an exemplary method fordetermining range information between vehicles in accordance with one ormore embodiments of the disclosure.

FIG. 3 is an exemplary graph illustrating a positioning technique inaccordance with one or more embodiments of the disclosure.

FIG. 4 is a schematic depiction of an interaction between vehicles inaccordance with one or more additional embodiments of the disclosure.

FIG. 5 is a schematic depiction of an interaction between vehicles inaccordance with one or more additional embodiments of the disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSURE

Embodiments of the disclosure relate to systems, methods, apparatuses,and computer-readable media for determining relative positioninginformation using one or more signal sensors and one or more signalsources. One or more specific embodiments of the disclosure relate tosystems, methods, apparatuses, and computer-readable media fordetermining one or more positions of a first vehicle with respect to asecond vehicle or vice versa, where the first vehicle has one or moresignal sensors associated therewith that detect one or more signalsreceived from one or more signal sources associated with the secondvehicle.

Embodiments of the disclosure are described more fully hereinafterthrough reference to the accompanying drawings, in which certainembodiments of the disclosure are shown. This disclosure may, however,be embodied in many different forms and should not be construed aslimited to the embodiments set forth herein; rather, these embodimentsare provided so that this disclosure will be thorough and complete, andfully convey the scope of the disclosed subject matter to those skilledin the art. Like numbers refer to like elements throughout.

Example embodiments of the disclosure will now be described withreference to the accompanying figures.

FIG. 1A is a schematic depiction of an interaction between two vehiclesemploying a system in accordance with one or more embodiments of thedisclosure. Throughout this disclosure, the term vehicle may refer to,but is not limited to, cars, motorcycles, mopeds, scooters, bicycles,other two-wheeled vehicles, all-terrain vehicles (ATVs), trucks,light-duty trucks, heavy-duty trucks, pickup trucks, minivans, crossoverutility vehicles (CUVs), vans, commercial vehicles, private vehicles,sport utility vehicles (SUVs), tractor-trailers, airplanes, helicopters,other aircraft, spacecraft, satellites, or any other suitable mobileobject provided with communicative and sensory capabilities. However, itshould be appreciated that embodiments of the disclosure may also beutilized in other transportation or non-transportation relatedapplications where electronic communications between two systems may beimplemented.

Further, throughout this disclosure the term “position” or “positionvector” may refer to a vector in three-dimensional space (e.g., <x, y,z>). Various embodiments of the disclosure relate to solving for thepositions of objects within a defined coordinate system. In one or moreembodiments of the disclosure, the z-coordinate may be known, in whichcase, techniques according to such embodiments may involve solving foronly the x and y coordinates of the position vector. In addition, in oneor more embodiments of the disclosure, the term “distance” may refer tothe hypotenuse (or magnitude) of a position vector.

Referring to FIG. 1A, a first vehicle 100A may have a signal sensor 102associated therewith. Referring to FIG. 1C, the signal sensor 102 mayform at least part of a signal detecting unit 108 associated with thevehicle 100A. The signal detecting unit 108 may additionally compriseone or more processors 109, a memory 110 operatively coupled to the oneor more processors 109, and a phase difference detector 111 operativelycoupled to the memory 110. The phase difference detector 111 and/or theone or more processors 109 may comprise one or more digital signalprocessors (DSPs). The first vehicle 100A may further comprise one ormore vehicle control units 112 and one or more input/output controlunits 113 configured to be controlled by the one or more processors 109.The one or more vehicle control units 112 may be configured to controloperations of one or more vehicle components 114. The one or moreinput/output control units 113 may be configured to control a userinterface (UI) 115 provided in connection with the vehicle 100A.

A second vehicle 100B may comprise three signal sources 101A-101C.Referring to FIGS. 1A and 1C, the signal sources 101A-101C may beconfigured to emit respective corresponding signals 118A-118C that maytravel along propagation paths 103A-103C, respectively. A coordinatesystem 104 may be defined in relation to the second vehicle 100B. Thecoordinate system 104 may have a center coordinate 104A located inproximity to the signal sources 101A-101C, such as, for example,vertically beneath the signal source 101B. However, in otherembodiments, the coordinate system 104 may be centered at any spatialposition in relative proximity to the signal sources 101A-101Cassociated with the vehicle 100B.

The signal sensor 102 associated with the vehicle 100A may be configuredto detect the signals 118A-118C received from the signal sources101A-101C, respectively. In accordance with one or more embodiments ofthe disclosure, the signal sources 101A-101C may each be any devicecapable of emitting radiation at any suitable wavelength, intensity, andcoherence. Radiation emitted by the signal sources 101A-101C may bemonochromatic or polychromatic and may be in the ultraviolet (UV),near-ultraviolet (near-UV), infrared (IR), or visible range. Forexample, in one or more embodiments of the disclosure, the signalsources 101A-101C may each be light-emitting diodes (LEDs) that emitradiation in the UV, near-UV, IR, or visible wavelength range.

In those embodiments in which the signal sources 101A-101C are LEDs,each LED may be electrically controlled to generate a pulsed signal. Forexample, referring to FIG. 1C, a signal generator 116 may be provided inconnection with the vehicle 100B that electrically controls the signalsources 101A-101C to synchronously emit the pulsed signals 118A-118C(e.g., the signal sources may turn on and off synchronously).

As previously described, each of the signal sources 101A-101C maytransmit a respective corresponding signal 118A-118C (e.g., rangingwaveform). The signals 118A-118C transmitted by the signal sources101A-101C may travel along the propagation paths 103A, 103B and 103C,respectively. The signals 118A-118C may be modulated using anyappropriate analog or digital modulation technique including, but notlimited to, amplitude modulation (AM) such as, for example,amplitude-shift keying (ASK) modulation; phase modulation such as, forexample, one or more forms of phase-shift keying (PSK); frequencymodulation such as, for example, one or more forms of frequency-shiftkeying (FSK); quadrature amplitude modulation (QAM); or any othermodulation technique. In certain embodiments of the disclosure, one ormore sub-carrier signals may be added to each of the signals 118A-118C,and the sub-carrier signal(s) may be phase modulated or frequencymodulated. In addition, the sub-carrier signal(s) may be modulated withorthogonal frequency-division multiplexing (OFDM). As a non-limitingexample, the signal sources 101A-101C may each represent LEDs that arepulsed to generate high frequency ON and OFF keyed waveforms. On-offkeying (OOK) is a form of ASK modulation that represents digital data asthe presence or absence of a carrier wave.

The signals 118A-118C may each be modulated with different OOKfrequencies which may be known to the signal detecting unit 108.Alternatively, in one or more embodiments of the disclosure, each of thesignal sources 101A-101C may emit respective corresponding signals118A-118C having a same OOK frequency. The signals 118A-118C may each bemodulated with a frequency in a range of about 20 MHz to about 70 MHz.However, other frequencies are also within the scope of the disclosure.Generally, the signals 118A-118C are modulated at a frequency that ishigh enough to permit a positioning technique to be used to analyze thesignals, but not so high as to cause phase aliasing. If a time of flightof the signals 118A-118C exceeds half of the period of the signals,phase aliasing may occur.

The signal detecting unit 108 may detect the signals 118A-118Crespectively emitted from the signal sources 101A-101C. Because thepropagation paths along which the signals 118A-118C respectively travelmay vary in length, the signals 118A-118C emitted by the signal sources101A-101C may reach the signal sensor 102 at different times. The phasedifference detector 111 may be configured to determine a phase shiftbetween each pair of the signals 118A-118C received by the signal sensor102. Specifically, the phase difference detector 111 may be configuredto process the signals 118A-118C in the frequency domain. That is, thephase difference detector 111 may be configured to measure the phaseshift of each of the signals 118A-118C with respect to each othersignal. For example, referring to FIG. 1E, the phase shift φ₁ betweenthe signal 118A and the signal 118B, the phase shift φ₂ between thesignal 118B and the signal 118C, and the phase shift φ₃ between thesignal 118A and the signal 118C may be measured by the phase differencedetector 111.

The phase shift or phase difference, in radians, between two signals maybe given by 2*π*f*τ, where f represents a frequency of the signals and τrepresents a time delay difference in receipt of the signals at a signalsensor due to different propagation paths taken by the signals. Thephase shifts φ₁, φ₂, φ₃ between each pair of the signals 118A-118C maybe measured by the phase difference detector 111 and may be communicatedto the one or more processors 109 of the signal detecting unit 108,which may be configured to determine, using the above relationship, aset of time values based on the measured phase shifts. The set of timevalues may represent a time delay difference between each pair ofreceived signals 118A-118C. For example, the set of time values mayinclude values τ₁, τ₂, and τ₃, representing a difference in a time ofreceipt or detection at the signal sensor 102 of the signals 118A and118B, the signals 118B and 118C, and the signals 118A and 118C,respectively.

For a sufficient signal-to-noise ratio (SNR), the phase differencedetector 111 may be capable of measuring a few degrees of phase shiftcorresponding to about 150 ps of delay. Determining the phase shiftbetween signals to this degree of accuracy may require an SNR of about40 dB and a detection bandwidth of about 100 Hz. The SNR present at thesignal sensor 102 may be influenced by various factors including, butnot limited to, the power of transmission of the signals 118A-118C, asize of a lens of the signal sensor 102, or the digital signal processordetection bandwidth.

The signal sensor 102 may be a starring array that is capable ofspatially separating the signals 118A-118C received from the signalsources 101A-101C in order for the phase difference detector 111 todetermine phase shifts between the signals 118A-118C. Referring to FIG.1E, the signal sensor 102 may be a non-imaging sensor array comprisingan optical lens 117. The signals 118A-118C may converge on one side ofthe lens 117 and be spatially separated on an opposing side of the lens.The signal sensor 102 may further comprise pixel sensors 119A-119C,where each pixel sensor detects a respective corresponding signal of thesignals 118A-118C. The phase difference detector 111 may measure thephase shift between the signals 118A-118C received at pixel sensors119A-119C.

It should be noted that the signal sensor 102 may also be an imagingsensor array having a suitable pixel density. Further, the signal sensor102 may be a scanning array that has a sufficiently high frame ratecapable of sampling the frequencies of the signals 118A-118C such thatthe phase shifts between the signals may be determined at receipt by thesignal sensor 102.

As will be described in more detail hereinafter, the one or moreprocessors 109 may be configured to generate a set of distanceexpressions. Each distance expression may represent a distance betweenone of the signal sources 101A-101C and the signal sensor 102. The oneor more processors 109 may be further configured to determine a set ofdistance equations based on the set of distance expressions and the setof time values. Additionally, the one or more processors 109 may befurther configured to solve the set of distance equations to determine aposition of the first vehicle 100A (e.g., a position of the signalsensor 102) within the coordinate system 104 defined in relation to thesecond vehicle 100B, or more specifically, in relation to the signalsources 101A-101C.

In one or more embodiments of the disclosure, the determined positionmay be utilized to facilitate cooperative driving, collision avoidance,and/or collision warning functionalities. As a non-limiting example, theone or more processors 109 may output the determined position to the oneor more vehicle control units 112, which may, in turn, control the oneor more vehicle components 114 to alter a velocity or an acceleration ofthe vehicle 100A, to initiate collision avoidance or collision safetymeasures, or to provide a warning indication to a user of the vehicle100A or to a user of the vehicle 100B. As another non-limiting example,the one or more processors 109 may output the determined position to theone or more input/output control units 113, which, in turn, may controla user interface 115 to provide a user (e.g., driver) of the vehicle100A with an indication of the determined position and one or morepotential warning indications. The user interface 115 may also providethe user of the vehicle 100A with functionality that allows the user tocontrol the one or more vehicle components 114 via the one or morevehicle control units 112 based on the determined position.

Three signal sources 101A-101C and one signal sensor 102 are shown inthe embodiment depicted in FIG. 1A. However, numerous otherconfigurations are within the scope of the disclosure. The vehicle 100Bmay have any number of signal sources associated therewith. Similarly,the vehicle 100A may have any number of signal sensors associatedtherewith. As a non-limiting example, in certain embodiments, thevehicle 100B may include one or more additional groups of three signalsources, and the vehicle 100A may include additional signal sensor(s)such that each group of three signal sources transmits respectivesignals to each signal sensor. As such, various configurations arewithin the scope of the disclosure that provide for determining multiplepositions of a vehicle in relation to another vehicle, which may beused, for example, to determine angular deviations or displacementsbetween vehicles. Further, although the signal sources 101A-101C aredepicted as being positioned at a front of the vehicle, otherconfigurations are within the scope of the disclosure. For example,additional signal sources may be positioned at the front, sides, roof,or rear of the vehicle 100B. Similarly, additional signal sensor(s) maybe positioned at the front, roof, sides, or rear of the vehicle 100A.

FIG. 1B depicts an interaction between two vehicles in accordance withone or more alternate embodiments of the disclosure. FIG. 1Bschematically depicts a first vehicle 100C having three signal sensors106A-106C associated therewith. Referring to FIG. 1D, the signal sensors106A-106C may form at least part of a signal detecting unit 120associated with the first vehicle 100C. A coordinate system 105 may bedefined in relation to the first vehicle 100C. The coordinate system 105may have a center coordinate 105A located in proximity to the signalsensors 106A-106C, such as, for example, vertically beneath the signalsensor 106B. However, numerous other configurations are within the scopeof the disclosure. The coordinate system 105 may be centered at anyspatial position within relative proximity of the signal sensors106A-106C. A signal source 128 may be associated with a second vehicle100D. The signal source 128 may emit a signal 130 that travels alongpropagation paths 107A-107C.

The signal detecting unit 120 associated with the vehicle 100C may beconfigured to detect the signal 130 received from the signal source 128.As previously described in connection with the embodiment of thedisclosure depicted in FIG. 1A, the signal source 128 may be any devicecapable of emitting radiation at any suitable wavelength, intensity, andcoherence. That is, radiation emitted by the signal source 128 may bemonochromatic or polychromatic and may be in the UV, near-UV, IR, orvisible range. For example, in one or more embodiments of thedisclosure, the signal source 128 may be an LED that emits radiation inthe UV, near-UV, IR, or visible wavelength range. The signal source 128may be electrically controlled to generate a pulsed signal. For example,referring to FIG. 1D, a signal generator 129 may be provided inconnection with the vehicle 100D that electrically controls the signalsource 128 to emit the pulsed signal 130. If more than one signal source128 is provided, the signal source(s) may be configured to turn on andoff synchronously.

The signal 130 emitted by the signal source 128 may be modulated usingany appropriate analog or digital modulation technique including, butnot limited to, amplitude modulation (AM) such as, for example,amplitude-shift keying (ASK) modulation; phase modulation such as, forexample, one or more forms of phase-shift keying (PSK); frequencymodulation such as, for example, one or more forms of frequency-shiftkeying (FSK); quadrature amplitude modulation (QAM); or any othermodulation technique. In certain embodiments of the disclosure, one ormore sub-carrier signals may be added to the signal 130, and thesub-carrier signal(s) may be phase modulated or frequency modulated. Inaddition, the sub-carrier signal(s) may be modulated with orthogonalfrequency-division multiplexing (OFDM). As a non-limiting example, thesignal source 128 may be an LED that is pulsed to generate highfrequency ON and OFF keyed waveforms. On-off keying (OOK) is a form ofASK modulation that represents digital data as the presence or absenceof a carrier wave.

In one or more embodiments of the disclosure, different OOK frequenciesmay be modulated onto the emitted signal 130. In one or more alternativeembodiments of the disclosure, the signal 130 emitted by the signalsource 128 may have a single OOK frequency.

The signal detecting unit 120 may further comprise one or moreprocessors 121, a memory 122 operatively coupled to the one or moreprocessors 121, and a phase difference detector 123 operatively coupledto the memory 122. The first vehicle 100C may further comprise one ormore vehicle control units 124 and one or more input/output controlunits 125 configured to be controlled by the one or more processors 121.The one or more vehicle control units 124 may be configured to controloperations of one or more vehicle components 126. The one or moreinput/output control units 125 may be configured to control a userinterface (UI) 127.

The signal 130 emitted by the signal source 128 may travel alongpropagation paths 107A-107C, respectively. Because each propagation pathmay vary in length, the signal 130 may reach the signal sensors106A-106C of the signal detecting unit 120 at different times. The phasedifference detector 123 of the signal detecting unit 120 may beconfigured to determine a phase shift or phase difference between thesignal at receipt or detection of the signal 130 by each of the signalsensors 106A-106C. The measured phase shifts may be communicated to theone or more processors 121 of the signal detecting unit 120, which maybe configured to determine a set of time values based on the measuredphase shifts.

The signal 130 may be modulated with a frequency in a range of about 20MHz to about 70 MHz. However, other frequencies are also within thescope of the disclosure. Generally, the signal 130 may be modulated at afrequency that is high enough to permit positioning techniques to beused to analyze the signal at a time of receipt by the signal sensors106A-106C, but not so high as to create phase aliasing. If a time offlight of the signal 130 along propagation paths 107A-107C exceeds halfof the period of the signal, phase aliasing may occur.

Similar to the embodiment of the disclosure depicted in FIG. 1A, thesignal detecting unit 120 may detect the signal 130 emitted from thesignal source 128. Because the signal 130 travels along propagationpaths 107A-107C that may vary in length, the signal 130 may reach eachof the signal sensors 106A-106C at different times. The phase differencedetector 123 may be configured to determine phase shifts between thesignals 130 received at signal sensors 106A-106C. Specifically, thephase difference detector 123 may be configured to process the receivedsignals 130 in the frequency domain. That is, the phase differencedetector 123 may be configured to measure the phase shift of the signal130 received at each of the signal sensors 106A-106C with respect to thesignal 130 received at each of the other signal sensors 106A-106C. Forexample, referring to FIG. 1F, the phase shift φ₁ between the signal 130received at the signal sensor 106A and the signal 130 received at thesignal sensor 106B, the phase shift φ₂ between the signal 130 receivedat the signal sensor 106B and the signal 130 received at the signalsensor 106C, and the phase shift φ₃ between the signal 130 received atthe signal sensor 106A and the signal 130 received at the signal sensor106C may be measured by the phase difference detector 123 in a mannersimilar to that previously described with respect to the embodimentdepicted in FIG. 1A.

The measured phase shifts φ₁, φ₂, φ₃ may be communicated by the phasedifference detector 123 via the memory 122 to the one or more processors121 of the signal detecting unit 120, which may be configured todetermine a set of time values based on the measured phase shifts. Eachvalue in the set of time values may represent a time delay differencebetween receipt of the signal 130 at one of the signal sensors 106A-106Cand receipt of the signal 130 at one of the other signal sensors106A-106C. For example, the set of time values may include values τ₁,τ₂, and τ₃, representing a difference in a time of receipt or detectionof the signal 130 at the signal sensors 106A and 106B, at the signalsensors 106B and 106C, and at the signal sensors 106A and 106C,respectively.

The one or more processors 121 may be configured to generate a set ofdistance expressions. Each distance expression may represent a distancebetween the signal source 128 and one of the signal sensors 106A-106C.The one or more processors 121 may be further configured to determine aset of distance equations based on the set of distance expressions andthe set of time values. Additionally, the one or more processors 121 maybe further configured to solve the set of distance equations todetermine a position associated with the second vehicle 100D (e.g., aposition of the signal source 128) within the coordinate system 105defined in relation to the first vehicle 100C, or more specifically, inrelation to the signal sensors 106A-106C.

In one or more embodiments of the disclosure, the determined positionmay be utilized to facilitate cooperative driving, collision avoidance,and/or collision warning functionalities. As a non-limiting example, theone or more processors 121 may output the determined position to the oneor more vehicle control units 124, which may, in turn, control the oneor more vehicle components 126 to alter a velocity or an acceleration ofthe vehicle 100C, to initiate collision avoidance or collision safetymeasures, or to provide a warning indication to a user of the vehicle100C or to a user of the vehicle 100D. As another non-limiting example,the one or more processors 121 may output the determined position to theone or more input/output control units 125, which, in turn, may controla user interface 127 to provide a user (e.g., driver) of the vehicle100C with an indication of the determined position and one or morepotential warning indications. The user interface 127 may also providethe user of the vehicle 100C with functionality that allows the user tocontrol the one or more vehicle components 126 via the one or morevehicle control units 124 based on the determined position.

The signal sensors 106A-106C may each be any photosensing orphotodetecting device known in the art including, but not limited to,photodiodes, optical detectors, LEDs that are reversed-biased to act asphotodiodes, phototransistors, photoresistors, phototubes, photovoltaiccells, quantum dot photoconductors, charge-coupled devices (CCD), oractive pixel sensors. The foregoing list is not intended as anexhaustive list, and any suitable signal sensors now known in the art orwhich may be developed in the future may be used.

Three signal sensors 106A-106C and one signal source 128 are shown inthe embodiment of the disclosure depicted in FIG. 1B. However, numerousother configurations are within the scope of the disclosure. The vehicle100D may have any number of signal sources associated therewith.Similarly, the vehicle 100C may have any number of signal sensorsassociated therewith. As a non-limiting example, in certain embodiments,the vehicle 100D may include one or more additional signal sources, andthe vehicle 100C may include additional groups of three signal sensorssuch that each group of three signal sensors receives a transmittedsignal from each signal source. In such a manner, multiple relativepositions between the vehicles 100C and 100D may be determined, whichmay, in turn, be used to determine angular deviations or displacementsbetween the vehicles 100C and 100D. Further, although the signal source128 is depicted as being positioned at the rear of the vehicle 100D,other configurations are within the scope of the disclosure. Forexample, additional signal sources may be positioned at the front,sides, roof, or rear of the vehicle 100D. Similarly, although the signalsensors 106A-106C are depicted as being positioned at the front of thevehicle 100C, additional signal sensor(s) may be positioned at thefront, roof, sides, or rear of the vehicle 100C.

In one or more embodiments of the disclosure, a packet structure may beemployed to convey information to a signal detecting unit, where theinformation relates to a respective corresponding signal source. Thediscussion below is applicable to one or more embodiments of thedisclosure, and thus will be presented in general terms withoutreference to any specific embodiment. A representative packet structureis depicted below:

Referring to the packet structure depicted above, the synchronizationfield may be used to obtain bit synchronization; the vehicle ID fieldmay comprise an identifier that uniquely identifies the vehicle withwhich the signal source is associated; and the <x, y, z> field maycomprise a spatial coordinate associated with the signal source which,as described earlier, may be a spatial coordinate within a coordinatesystem defined in relation to a vehicle. The remaining field depicted inthe packet structure above may refer to the signal emitted from thesignal source. Although the signal is referred to as an OOK RangingWaveform, the signal may be modulated according to any of the modulationschemes previously described. In one or more embodiments of thedisclosure, the synchronization field, the vehicle ID field, and thesignal source spatial coordinate field may be transmitted via modulationof the signal emitted from the signal source. As a non-limiting example,the signal emitted from a signal source may be frequency modulated usingany appropriate modulation scheme (e.g., frequency-shift on and offkeying (OOK), Manchester encoding, and so forth) to convey digital datarelating to the other non-ranging fields.

Embodiments of the disclosure provide several advantages overconventional systems. For example, embodiments of the disclosure relateto positioning systems and techniques for determining relativepositioning information between vehicles that provide the accuracy ofLIDAR, for example, at the relatively inexpensive costs associated withSONAR, for example. Further, ranging technologies such as LIDAR, RADARand SONAR are incapable of determining positioning information betweenobjects in accordance with embodiments of the disclosure. LIDAR, forexample, is only capable of determining range information; spatial orangular relationships must be determined indirectly based on thedirectionality of the laser.

Any of the signal sources 101A-101C of the embodiment depicted in FIG.1A or the signal source 128 of the embodiment depicted in FIG. 1B may beprovided as part of signaling lights of the vehicles 100B and 100D,respectively. More specifically, the signal sources 101A-101C or thesignal source 128 may each be LEDs that are provided as part of one ormore vehicle signaling lights. The one or more signaling lights may beany suitable signaling lights including, but not limited to, taillights, brake lights, reverse lights, headlights, side lights, mirrorlights, fog lamps, low beams, high beams, add-on lights, or combinationsthereof. Alternatively, the signal sources 101A-101C may be positionedon the vehicle 100B or the signal source 128 may be positioned on thevehicle 100D independent of any signaling lights and may be configuredto emit non-visible radiation such that a vehicle operator does notconfuse the emitted radiation with other indications provided by thesignaling lights.

The signal sources 101A-101C or the signal source 128 may include, butare not limited to, LEDs, incandescent lamps, halogen lamps, fluorescentlamps, compact fluorescent lamps, gas discharge lamps, lightamplification by stimulated emission of radiation (lasers), diodelasers, gas lasers, solid state lasers, or combinations thereof.

The one or more processors 109 or the one or more processors 121 mayinclude, without limitation, a central processing unit (CPU), a digitalsignal processor (DSP), a reduced instruction set computer (RISC), acomplex instruction set computer (CISC), a microprocessor, amicrocontroller, a field programmable gate array (FPGA), or anycombination thereof. The one or more processors 109 or the one or moreprocessors 121 may be from a family of Intel® processors, such as theIntel® Atom® processor family. The one or more processors 109 or the oneor more processors 121 may also include one or more application-specificintegrated circuits (ASICs) or application-specific standard products(ASSPs) for handling specific data processing functions or tasks.

In certain embodiments, the one or more processors 109 or the one ormore processors 121 may be a part of a general vehicle main computersystem. The main computer system may, in various embodiments of thedisclosure, manage various aspects of the operation of the vehicle, suchas engine control, transmission control, and various component controls.In other embodiments, the signal detecting unit 108 or the signaldetecting unit 120 may be separate and stand-alone systems that controlinter-vehicle communications. Additionally, in certain embodiments, thesignal detecting unit 108 or the signal detecting unit 120 may beintegrated into the vehicle, while in other embodiments, may be added tothe vehicle following production and/or initial configuration of thevehicle.

The memory 110 or 122 may include one or more volatile and/ornon-volatile memory devices including, but not limited to, magneticstorage devices, random access memory (RAM), dynamic RAM (DRAM), staticRAM (SRAM), synchronous dynamic RAM (SDRAM), double data rate (DDR)SDRAM (DDR-SDRAM), RAM-BUS DRAM (RDRAM), flash memory devices,electrically erasable programmable read-only memory (EEPROM),non-volatile RAM (NVRAM), universal serial bus (USB) removable memory,or combinations thereof.

The user interface 115 or the user interface 127 may be any known inputdevice, output device, or input and output device that can be used by auser to communicate with the one or more processors 109 or the one ormore processors 121, and may include, but are not limited to, a touchpanel, a keyboard, a display, a speaker, a switch, a visual indicator,an audio indicator, a tactile indicator, a speech to text engine, orcombinations thereof. In one or more embodiments of the disclosure, theuser interface 115 or the user interface 127 may be used by a user, suchas a driver of the vehicle 100A or a driver of the vehicle 100C, toselectively activate or deactivate the signal detecting unit 108 or thesignal detecting unit 120, respectively. In other embodiments of thedisclosure, the user interface 115 or the user interface 127 may beemployed to control the one or more processors 109 or the one or moreprocessors 121 to provide one or more control signals to the one or morevehicle control units 112 or the one or more vehicle control units 124,respectively, to control the one or more components 114 of the vehicle100A or the one or more components 126 of the vehicle 100C. The one ormore vehicle components 114 or the one or more vehicle components 126may include, but are not limited to, brakes, an engine, a transmission,a fuel supply, a throttle valve, a clutch, or any combination thereof.

FIG. 2 depicts an exemplary method for determining position informationbetween vehicles using a Time Difference of Arrival (TDOA) technique.The TDOA technique will be described through reference to the embodimentdepicted in FIG. 1A in which the signal sensor 102 associated with thevehicle 100A receives three signals 118A-118C from the respectivecorresponding three signal sources 101A-101C associated with the vehicle100B. However, it should be appreciated that methods according toembodiments of the disclosure are applicable to any configuration ofsignal sensor(s) and signal source(s) including, but not limited to, theembodiment of the disclosure depicted in FIG. 1B.

Referring to FIG. 2, at block 201, the phase difference detector 111measures phase shifts φ₁, φ₂, φ₃ between the signal 118A and the signal118B, between the signal 118B and the signal 118C, and between thesignal 118A and the signal 118C, respectively. The phase differencedetector 111 communicates the measured phase shifts to the one or moreprocessors 109 of the signal detecting unit 108, which may be configuredto determine a set of time values based on the measured phase shifts. Aspreviously described, the set of time values may represent a time delaydifference between each pair of received signals 118A-118C.

At block 203, the one or more processors 109 may be configured toexecute one or more computer program instructions stored, for example,in the memory 110 to generate a set of distance expressions, where eachdistance expression represents a distance between one of the signalsources 101A-101C and the signal sensor 102 within the coordinate system104. For example, the set of distance expressions may comprise analgebraic representation of a distance between the signal source 101Aand the signal sensor 102, a distance between the signal source 101B andthe signal sensor 102, and a distance between the signal source 101C andthe signal sensor 102.

At block 204, the one or more processors 109 may be further configuredto execute one or more computer program instructions stored, forexample, in the memory 110 to generate a set of distance equations basedon the set of distance expressions and the set of time values. Eachdistance equation may represent a difference between one distanceexpression and one other distance expression and may be equivalent to atime delay between receipt of one of the signals 118A-118C and one ofthe other signals 118A-118C (e.g., τ₁, τ₂, or τ₃) multiplied by avelocity of the signals 118A-118C.

At block 205, the one or more processors 109 may be configured toexecute one or more computer program instructions stored, for example,in the memory 110 to solve the set of distance equations to determineone or more positions of the first vehicle 100A in relation to thecoordinate system 104 defined with respect to the second vehicle 100B.More specifically, the one or more processors 109 may be configured tosolve the set of distance equations using a TDOA hyperbolic positioningtechnique.

An exemplary algebraic derivation according to one or more embodimentsof the disclosure will now be described in more detail. The exemplaryderivation is presented in the context of the embodiment of thedisclosure depicted in FIG. 1A. However, one of ordinary skill in theart will recognize that the technique described below is applicable toany embodiment of the disclosure and that other techniques fordetermining positions between vehicles having one or more signal sourcesand one or more signal sensors associated therewith are within the scopeof the disclosure.

Let A_(i), A_(j), and A_(k) represent the three signal sources101A-101C, respectively. A_(i), A_(j), and A_(k) may be assigned spatialcoordinates <x_(i), y_(i), z_(i)>, <x_(j), y_(j), z_(j)>, and <x_(k),y_(k), z_(k)>, respectively, with respect to the coordinate plane 104.Further, Let A_(t) represent the signal sensor 102. The signal sensorA_(t) may be assigned a spatial coordinate <x_(t), y_(t), z_(t)> withrespect to the coordinate system 104. According to embodiments of thedisclosure, a starting point for a TDOA technique for determining one ormore distances between vehicles (e.g., vehicle 100A and vehicle 100B) isthe equation for the distance between two points.R=√{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i) −z_(t))²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i)−z _(t))²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z_(i) −z _(t))²)}  Eq. 1

The distance between an emitting source and a receiving sink may bedetermined indirectly by determining a time of arrival (TOA) of a signalreceived by the receiving sink from the emitting source. Multiplying theTOA t by the signal velocity c (e.g., the speed of light in air) yieldsa distance of travel R. Equation 1 may be expanded to three distanceexpressions based upon vector coordinates associated with the signalsources A_(i), A_(j), and A_(k) and the vector coordinate associatedwith the signal sensor A_(t).ct _(i) =R _(i)=√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))²+(z _(i) −z _(t))²)}{square root over ((x _(i) −x _(t))²+(y _(i)−y _(t))²+(z _(i) −z _(t))²)}{square root over ((x _(i) −x _(t))²+(y_(i) −y _(t))²+(z _(i) −z _(t))²)}  Eq. 2ct _(j) =R _(j)=√{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))²+(z _(j) −z _(t))²)}{square root over ((x _(j) −x _(t))²+(y _(j)−y _(t))²+(z _(j) −z _(t))²)}{square root over ((x _(j) −x _(t))²+(y_(j) −y _(t))²+(z _(j) −z _(t))²)}  Eq. 3ct _(k) =R _(k)=√{square root over ((x _(k) −x _(t))²+(y _(k) −y_(t))²+(z _(k) −z _(t))²)}{square root over ((x _(k) −x _(t))²+(y _(k)−y _(t))²+(z _(k) −z _(t))²)}{square root over ((x _(k) −x _(t))²+(y_(k) −y _(t))²+(z _(k) −z _(t))²)}  Eq. 4

For the purposes of this exemplary derivation, distances along thez-axis of the coordinate system 104 are assumed to be known. As such,referring to FIG. 3, the following derivation yields a system 300 of twoequations with each equation describing a respective hyperbolic function301, 302. An intersection 303 of the two hyperbolic functions 301, 302represents a position of A_(t) (e.g., the signal sensor 102) withrespect to the signal sources A_(i), A_(j), and A_(k), or morespecifically, within the coordinate system 104.

Equations 2, 3, and 4 may be used to generate distance equationscorresponding to the distance differences R_(ji), R_(ki), and R_(kj),where:R _(j) −R _(i) =R _(ji) =c(t _(j) −t _(i))=√{square root over ((x _(j)−x _(t))²+(y _(j) −y _(t))²+(z _(j) −z _(t))²)}{square root over ((x_(j) −x _(t))²+(y _(j) −y _(t))²+(z _(j) −z _(t))²)}{square root over((x _(j) −x _(t))²+(y _(j) −y _(t))²+(z _(j) −z _(t))²)}−√{square rootover ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i) −z _(t))²)}{squareroot over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i) −z_(t))²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i)−z _(t))²)}  Eq. 5R _(k) −R _(i) =R _(ki) =c(t _(k) −t _(i))=√{square root over ((x _(k)−x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}{square root over ((x_(k) −x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}{square root over((x _(k) −x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}−√{square rootover ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i) −z _(t))²)}{squareroot over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i) −z_(t))²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))²+(z _(i)−z _(t))²)}  Eq. 6R _(k) −R _(j) =R _(kj) =c(t _(k) −t _(j))=√{square root over ((x _(k)−x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}{square root over ((x_(k) −x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}{square root over((x _(k) −x _(t))²+(y _(k) −y _(t))²+(z _(k) −z _(t))²)}−√{square rootover ((x _(j) −x _(t))²+(y _(j) −y _(t))²+(z _(j) −z _(t))²)}{squareroot over ((x _(j) −x _(t))²+(y _(j) −y _(t))²+(z _(j) −z_(t))²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y _(t))²+(z _(j)−z _(t))²)}  Eq. 7

As the distance differences R_(ji), R_(ki), and R_(kj) are eachequivalent to the time delay between the receipt or detection, at thesignal sensor 102, of one of the signals 118A, 118B, or 118C and one ofthe other signals 118A, 118B, or 118C multiplied by the velocity of thesignals 118A-118C, the values of the distance differences R_(ji),R_(ki), and R_(kj) may be determined based on the set of time valuesdetermined at block 202 (FIG. 2), which, in turn, may be determinedbased on the phase shifts between the signals measured at block 201.

As previously discussed, for the purposes of the positioning techniquedetailed below, distances between the vehicles along the z axis areassumed to be known constants. However, one of ordinary skill in the artwill appreciate that embodiments in which the distances along the z-axisare not known constants are also within the scope of the disclosure, andthat this exemplary derivation may be extended to encompass suchembodiments.

Assuming that distance differences along the z-axis are known constants,those distance differences may be replaced with algebraic symbols thatrepresent constants as shown below in Equation 8.z _(jt)=(z _(j) −z _(t)), z _(it)=(z _(i) −z _(t)) and z _(kt)=(z _(k)−z _(t)).  Eq. 8

Substituting in the constants provided by Equation 8 and moving onesquare root term to the other side for each of Equations 5, 6, and 7yields:R _(ji)+√{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it)²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it)²)}=√{square root over ((x _(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt)²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt)²)}  Eq. 9R _(ki)+√{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it)²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it)²)}=√{square root over ((x _(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt)²)}{square root over ((x _(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt)²)}  Eq. 10R _(kj)+√{square root over ((x _(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt)²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt)²)}=√{square root over ((x _(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt)²)}{square root over ((x _(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt)²)}  Eq. 11

Squaring both sides of each of Equations 9, 10, and 11 produces thefollowing set of equations:R _(ji) ²+2R _(ji)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+(x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it) ²=(x_(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt) ²  Eq. 12R _(ki) ²+2R _(ki)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+(x _(i) −x _(t))²+(y _(i) −y _(t))² +z _(it) ²=(x_(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt) ²  Eq. 13R _(kj) ²+2R _(kj)√{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}+(x _(j) −x _(t))²+(y _(j) −y _(t))² +z _(jt) ²=(x_(k) −x _(t))²+(y _(k) −y _(t))² +z _(kt) ²  Eq. 14

Expanding the remaining squared terms in each of Equations 12, 13, and14 produces:R _(ji) ²+2R _(ji)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+x _(i) ²−2x _(i) x _(t) −x _(t) ² +y _(i) ²−2y _(i)y _(t) −y _(t) ² +z _(it) ² =x _(j) ²2x _(j) x _(t) −x _(t) ² +y _(j)²−2y _(j) y _(t) −y _(t) ² +z _(jt) ²  Eq. 15R _(ki) ²+2R _(ki)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+x _(i) ²−2x _(i) x _(t) −x _(t) ² +y _(i) ²−2y _(i)y _(t) −y _(t) ² +z _(it) ² =x _(k) ²2x _(k) x _(t) −x _(t) ² +y _(k)²−2y _(k) y _(t) −y _(t) ² +z _(kt) ²  Eq. 16R _(kj) ²+2R _(kj)√{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}+x _(j) ²−2x _(j) x _(t) −x _(t) ² +y _(j) ²−2y _(j)y _(t) −y _(t) ² +z _(jt) ² =x _(k) ²2x _(k) x _(t) −x _(t) ² +y _(k)²−2y _(k) y _(t) −y _(t) ² +z _(kt) ²  Eq. 17

Eliminating the x_(t) ² and y_(t) ² from both sides of each of Equations15, 16, and 17 reduces the equation set to the following equations:R _(ji) ²+2R _(ji)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+x _(i) ²−2x _(i) x _(t) +y _(i) ²−2y _(i) y _(t) +z_(it) ² =x _(j) ²−2x _(j) x _(t) +y _(j) ²−2y _(j) y _(t) +z _(jt)²  Eq. 18R _(ki) ²+2R _(ki)√{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}{square root over ((x _(i) −x _(t))²+(y _(i) −y_(t))² +z _(it) ²)}+x _(i) ²−2x _(i) x _(t) +y _(i) ²−2y _(i) y _(t) +z_(it) ² =x _(k) ²−2x _(k) x _(t) +y _(k) ²−2y _(k) y _(t) +z _(ki)²  Eq. 19R _(kj) ²+2R _(kj)√{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}{square root over ((x _(j) −x _(t))²+(y _(j) −y_(t))² +z _(jt) ²)}+x _(j) ²−2x _(j) x _(t) +y _(j) ²−2y _(j) y _(t) +z_(jt) ² =x _(k) ²−2x _(k) x _(t) +y _(k) ²−2y _(k) y _(t) +z _(kt)²  Eq. 20

Shifting all but the square root terms to the right side of each ofEquations 18, 19, and 20 and combining similar terms yields:

$\begin{matrix}{\sqrt{\left( {x_{i} - x_{t}} \right)^{2} + \left( {y_{i} - y_{t}} \right)^{2} + z_{it}^{2}} = \frac{\mspace{31mu}{{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right) + {2{x\left( {x_{i} - x_{j}} \right)}} + {2{y\left( {y_{i} - y_{j}} \right)}}}}{2R_{ji}}} & {{Eq}.\mspace{14mu} 21} \\{\sqrt{\left( {x_{i} - x_{t}} \right)^{2} + \left( {y_{i} - y_{t}} \right)^{2} + z_{it}^{2}} = \frac{\mspace{34mu}{{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right) + {2{x\left( {x_{i} - x_{k}} \right)}} + {2{y\left( {y_{i} - y_{k}} \right)}}}}{2R_{ki}}} & {{Eq}.\mspace{14mu} 22} \\{\sqrt{\left( {x_{j} - x_{t}} \right)^{2} + \left( {y_{j} - y_{t}} \right)^{2} + z_{jt}^{2}} = \frac{\mspace{34mu}{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2{x\left( {x_{j} - x_{k}} \right)}} + {2{y\left( {y_{j} - y_{k}} \right)}}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

Equations 21, 22 and 23 may now be simplified by making the followingvariable substitutions: x_(ij) for x_(i)−x_(j) and y_(ij) fory_(i)−y_(j).

$\begin{matrix}{\sqrt{\left( {x_{i} - x_{t}} \right)^{2} + \left( {y_{i} - y_{t}} \right)^{2} + z_{it}^{2}} = \frac{{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \mspace{31mu}\left( {z_{jt}^{2} - z_{it}^{2}} \right) + {2{xx}_{ij}} + {2{yy}_{ij}}}{2R_{ji}}} & {{Eq}.\mspace{14mu} 24} \\{\sqrt{\left( {x_{i} - x_{t}} \right)^{2} + \left( {y_{i} - y_{t}} \right)^{2} + z_{it}^{2}} = \frac{{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \mspace{25mu}\left( {z_{kt}^{2} - z_{it}^{2}} \right) + {2{xx}_{ik}} + {2{yy}_{ik}}}{2R_{ki}}} & {{Eq}.\mspace{14mu} 25} \\{\sqrt{\left( {x_{j} - x_{t}} \right)^{2} + \left( {y_{j} - y_{t}} \right)^{2} + z_{jt}^{2}} = \frac{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \mspace{25mu}\left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2{xx}_{jk}} + {2{yy}_{jk}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

Through the above-described algebraic manipulations, Equations 5-7 havebeen transformed into Equations 24-26 that, when squared, representintersecting hyperboloids. By equating Equation 24 and Equation 25 toform Equation 27, we can derive a plane equation in the form of y=Ax+C.Equating Equations 24 and 25 yields:

$\begin{matrix}{\frac{{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right) + {2x_{t}x_{ij}} + {2{yy}_{ij}}}{2R_{ji}} = \frac{{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right) + {2x_{t}x_{ik}} + {2{yy}_{ik}}}{2R_{ki}}} & {{Eq}.\mspace{14mu} 27}\end{matrix}$

Multiplying both sides of Equation 27 by R_(ki) and separatingfractional components yields:

$\begin{matrix}{{\frac{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack}{2} + {R_{ki}\left( {{x_{t}x_{ij}} + {y_{t}y_{ij}}} \right)}} = {\frac{R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}{2} + {R_{ji}\left( {{x_{t}x_{ik}} + {y_{t}y_{ik}}} \right)}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$

Moving certain terms between both sides of Equation 28 yields:

$\begin{matrix}{\frac{{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack} - {- {R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}}}{2} = {{+ {R_{ji}\left( {{x_{t}x_{ik}} + {y_{t}y_{ik}}} \right)}} - {R_{ki}\left( {{x_{t}x_{ij}} + {y_{t}y_{ij}}} \right)}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$

Rearranging and factoring out certain terms from the left side ofEquation 29 yields:

$\begin{matrix}{{{x_{t}\left( {{R_{ji}x_{ik}} - {R_{ki}x_{ij}}} \right)} + {y_{t}\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)}} = \frac{{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack} - \mspace{11mu}{R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}}{2}} & {{Eq}.\mspace{14mu} 30}\end{matrix}$

Moving the term x_(t)(R_(ji)x_(ik)−R_(ki)x_(ij)) from the left side ofEquation 30 to the right side yields:

$\begin{matrix}{{y_{t}\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)} = {{- {x_{t}\left( {{R_{ji}x_{ik}} - {R_{ki}x_{ij}}} \right)}} + \frac{{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack} - \mspace{11mu}{R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}}{2}}} & {{Eq}.\mspace{14mu} 31}\end{matrix}$

Dividing both sides of Equation 31 by (R_(ji)y_(ik)−R_(ki)y_(ij))yields:

$\begin{matrix}{y_{t} = {{x_{t}\frac{\left( {{{- R_{ji}}x_{ik}} + {R_{ki}x_{ij}}} \right)}{\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)}} + \frac{{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack} - \mspace{11mu}{R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}}{2\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)}}} & {{Eq}.\mspace{14mu} 32}\end{matrix}$

Equation 32 is now in the desired form of a general plane equation givenby Equation 33 below:

$\begin{matrix}{{y_{t} = {{Ax}_{t} + C}}{where}} & {{Eq}.\mspace{14mu} 33} \\{{A = \frac{\left( {{R_{ki}x_{ij}} - {R_{ji}x_{ik}}} \right)}{\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)}}{and}} & {{Eq}.\mspace{14mu} 34} \\{C = \frac{{R_{ki}\left\lbrack {{- R_{ji}^{2}} + \left( {x_{j}^{2} - x_{i}^{2}} \right) + \left( {y_{j}^{2} - y_{i}^{2}} \right) + \left( {z_{jt}^{2} - z_{it}^{2}} \right)} \right\rbrack} - \mspace{11mu}{R_{ji}\left\lbrack {{- R_{ki}^{2}} + \left( {x_{k}^{2} - x_{i}^{2}} \right) + \left( {y_{k}^{2} - y_{i}^{2}} \right) + \left( {z_{kt}^{2} - z_{it}^{2}} \right)} \right\rbrack}}{2\left( {{R_{ji}y_{ik}} - {R_{ki}y_{ij}}} \right)}} & {{Eq}.\mspace{14mu} 35}\end{matrix}$

Substituting Equation 33 back into Equation 26 yields Equation 36 below.

$\begin{matrix}{\sqrt{\left( {x_{j} - x_{t}} \right)^{2} + \left( {y_{j} - {Ax}_{t} - C} \right)^{2} + z_{jt}^{2}} = \frac{\mspace{25mu}{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2x_{t}x_{jk}} + {2\left( {{Ax}_{t} + C} \right)y_{jk}}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 36}\end{matrix}$

Rearranging and expanding certain terms on the left side of Equation 36yields:

$\begin{matrix}{\sqrt{x_{j}^{2} - {2x_{t}x_{j}} + x_{t}^{2} + {A^{2}x_{t}^{2}} - {2{{Ax}_{t}\left( {y_{j} - C} \right)}} + \left( {y_{j} - C} \right)^{2} + z_{jt}^{2}} = \frac{\mspace{20mu}{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2x_{t}x_{jk}} + {2\left( {{Ax}_{t} + C} \right)y_{jk}}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 37}\end{matrix}$

Multiplying certain terms through on the right side of Equation 37yields:

$\begin{matrix}{\sqrt{x_{j}^{2} - {2x_{t}x_{j}} + x_{t}^{2} + {A^{2}x_{t}^{2}} - {2{{Ax}_{t}\left( {y_{j} - C} \right)}} + \left( {y_{j} - C} \right)^{2} + z_{jt}^{2}} = \frac{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + \mspace{85mu}{2x_{t}x_{jk}} + {2y_{jk}{Ax}_{t}} + {2{Cy}_{jk}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 38}\end{matrix}$

Factoring out like terms, regrouping certain terms, and separatingfractional terms on the right side of Equation 38 yields:

$\begin{matrix}{\sqrt{{x_{t}^{2}\left( {1 + A^{2}} \right)} + {x_{t}\left( {{{- 2}x_{j}} - {2{A\left( {y_{j} - C} \right)}}} \right)} + \left( {x_{j}^{2} + \left( {y_{j} - C} \right)^{2} + z_{jt}^{2}} \right)} = {\frac{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2{Cy}_{jk}}}{2R_{kj}} + {x_{t}\frac{x_{jk} + {y_{jk}A}}{R_{kj}}}}} & {{Eq}.\mspace{14mu} 39}\end{matrix}$

Alternate symbols may now be used to represent constant terms inEquation 39:

$\begin{matrix}{D = {1 + A^{2}}} & {{Eq}.\mspace{14mu} 40} \\{E = {{{- 2}x_{j}} - {2{A\left( {y_{j} - C} \right)}}}} & {{Eq}.\mspace{14mu} 41} \\{F = {x_{j}^{2} + \left( {y_{j} - C} \right)^{2} + z_{jt}^{2}}} & {{Eq}.\mspace{14mu} 42} \\{G = \frac{x_{jk} + {y_{jk}A}}{R_{kj}}} & {{Eq}.\mspace{14mu} 43} \\{H = \frac{{- R_{kj}^{2}} + \left( {x_{k}^{2} - x_{j}^{2}} \right) + \left( {y_{k}^{2} - y_{j}^{2}} \right) + \left( {z_{kt}^{2} - z_{jt}^{2}} \right) + {2{Cy}_{jk}}}{2R_{kj}}} & {{Eq}.\mspace{14mu} 44}\end{matrix}$

The symbols of Equations 40-44 may now be substituted into Equation 39to yield:√{square root over (x _(t) ² D+x _(t) E+F)}=x _(t) G+H  Eq. 45

Squaring both sides of Equation 45 yields:x _(t) ² D+x _(t) E+F=x _(t) ² G ²+2x _(t) GH+H ²  Eq. 46

Factoring out like terms and rearranging terms between both sides ofEquation 46 yields:x _(t) ²(D−G ²)+x _(t)(E−2GH)+(F−H ²)=0  Eq. 47

Alternate symbols may be used to simplify Equation 47 as follows:J=D−G ²  Eq. 48K=E−2GH  Eq. 49L=F−H ²  Eq. 50

Substituting the alternate symbols from Equations 48-50 into Equation 47yields:x _(t) ² J+x _(t) K+L=0  Eq. 51

Equation 51 is now in the form of a quadratic equation. It is nowpossible to solve for x_(t) using the quadratic formula shown below.

$\begin{matrix}{x_{t} = \frac{{- K} \pm \sqrt{K^{2} - {4{JL}}}}{2J}} & {{Eq}.\mspace{14mu} 52}\end{matrix}$

Solving for x_(t) may yield both a positive and a negative root. Byconvention, it may be determined that the negative root indicates thatthe vehicle 100A is positioned behind the vehicle 100B. Similarly, apositive root may indicate that the vehicle 100A is positioned in frontof the vehicle 100B. Other conventions may be used according to one ormore alternate embodiments of the disclosure. Equation 52 may besubstituted back into equation 33 to solve for y_(t). Because it isassumed that the distances between the signal sensor 102 and the signalsources 101A-101C along the z-axis are known, and thus that z_(t) (whichrepresents a z-coordinate of the signal sensor A_(t) with respect to thecoordinate system 104) is known, solving for x_(t) and y_(t) will yieldthe spatial coordinate <x_(i), y_(t), z_(t)> for the signal sensor A_(t)(e.g., the signal sensor 102) within the coordinate system 104.Determining the spatial coordinate <x_(t), y_(t), z_(t)> for the signalsensor A_(t) within the coordinate system 104 provides a measure of aposition of the vehicle 100A in relation to the vehicle 100B.

Although the above positioning technique has been described throughreference to the embodiment of the disclosure depicted in FIG. 1A, thetechnique is equally applicable to other embodiments of the disclosure,including the embodiment depicted in FIG. 1B as well as otherembodiments in which additional signal source(s) and additional signalsensor(s) are provided.

FIG. 4 depicts certain embodiments of the disclosure in which multiplesignal sources and multiple signal sensors are used to determinemultiple positions between a vehicle 400A and a vehicle 400B. In one ormore embodiments of the disclosure, elements 402A-402C may representthree signal sources associated with the vehicle 400B. The signalsources 402A-402C may be of a type previously described. Elements401A-401C may represent three signal sensors associated with the vehicle400A. The signal sensors 401A-401C may be of a type previouslydescribed. Each of the signal sensors 401A-401C may receive a signalfrom each of the signal sources 402A-402C. Using the techniquepreviously described, a position associated with each of the signalsources 402A-402C within a coordinate system defined in relation tovehicle 400A may be determined. An angular deviation and displacement ofvehicle 400B with respect to vehicle 400A may be determined based on thedetermined position(s).

In one or more alternate embodiments of the disclosure, elements402A-402C may represent three signal sensors associated with the vehicle400B. The signal sensors 402A-402C may be of a type previouslydescribed. Elements 401A-401C may represent three signal sourcesassociated with the vehicle 400A. The signal sources 401A-401C may be ofa type previously described. Each of the signal sensors 402A-402C mayreceive a signal from each of the signal sources 401A-401C. Using thetechnique previously described, a position associated with each of thesignal sensors 402A-402C within a coordinate system defined in relationto the vehicle 400A may be determined. An angular deviation anddisplacement of vehicle 400B with respect to vehicle 400A may bedetermined based on the determined position(s).

The one or more positions between vehicles, determined using thepositioning technique described above, may represent slant positionsbetween the vehicles. Referring to FIG. 5, for example, one or morepositions of a vehicle 500C in relation to a vehicle 500D, or viceversa, may be determined based on a positioning technique according toembodiments of the disclosure, and may represent slant positions betweenthe vehicle 500C and the vehicle 500D. The slant positions may bedefined along a reference plane that may extend through origins ofcoordinate systems associated with the vehicles 500C and 500D. Aspreviously discussed, the height separation 503 between the vehicle 500Cand the vehicle 500D may represent a known distance (a constant) along az-axis of a coordinate plane defined in relation to the vehicle 500C orthe vehicle 500D.

Embodiments described herein may be implemented using hardware,software, and/or firmware, for example, to perform the methods and/oroperations described herein. Certain embodiments described herein may beprovided as a tangible, non-transitory machine-readable medium storingmachine-executable instructions that, if executed by a machine, causethe machine to perform the methods and/or operations described herein.The tangible machine-readable medium may include, but is not limited to,any type of disk including floppy disks, optical disks, compact diskread-only memories (CD-ROMs), compact disk rewritables (CD-RWs), andmagneto-optical disks, semiconductor devices such as read-only memories(ROMs), random access memories (RAMs) such as dynamic and static RAMs,erasable programmable read-only memories (EPROMs), electrically erasableprogrammable read-only memories (EEPROMs), flash memories, magnetic oroptical cards, or any type of tangible media suitable for storingelectronic instructions. The machine may include any suitable processingor computing platform, device, or system and may be implemented usingany suitable combination of hardware and/or software. The instructionsmay include any suitable type of code and may be implemented using anysuitable programming language. In certain embodiments,machine-executable instructions for performing the methods and/oroperations described herein may be embodied in software embodied in anyof one or more higher-level programming languages capable of beingcompiled or interpreted, microcode, or firmware.

Various features, aspects, and embodiments have been described herein.The features, aspects, and embodiments are susceptible to combinationwith one another as well as to variation and modification, as will beunderstood by those having skill in the art. The present disclosureshould, therefore, be considered to encompass such combinations,variations, and modifications.

The terms and expressions which have been employed herein are used asterms of description and not of limitation. In the use of such terms andexpressions, there is no intention of excluding any equivalents of thefeatures shown and described (or portions thereof), and it is recognizedthat various modifications are possible within the scope of the claims.Other modifications, variations, and alternatives are also possible.Accordingly, the claims are intended to cover all such equivalents.

While certain embodiments of the disclosure have been described inconnection with what is presently considered to be the most practicaland various embodiments, it is to be understood that the disclosure isnot to be limited to the disclosed embodiments, but on the contrary, isintended to cover various modifications and equivalent arrangementsincluded within the scope of the claims. Although specific terms areemployed herein, they are used in a generic and descriptive sense only,and not for purposes of limitation.

This written description uses examples to disclose certain embodimentsof the disclosure, including the best mode, and also to enable anyperson skilled in the art to practice certain embodiments of thedisclosure, including making and using any devices or systems andperforming any incorporated methods. The patentable scope of certainembodiments of the disclosure is defined in the claims, and may includeother examples that occur to those skilled in the art. Such otherexamples are intended to be within the scope of the claims if they havestructural elements that do not differ from the literal language of theclaims, or if they include equivalent structural elements withinsubstantial differences from the literal language of the claims.

What is claimed is:
 1. A method, comprising: detecting, at a signaldetecting unit associated with a first vehicle, one or more signalsreceived from one or more signal sources, the signal detecting unitcomprising one or more signal sensors and one or more computerprocessors; determining, by the one or more computer processors, a setof time values based on arrival times of the one or more signals;generating, by the one or more computer processors, a set of distanceexpressions, wherein each distance expression corresponds to a distancebetween one of the one or more signal sensors and one of the one or moresignal sources; generating, by the one or more computer processors, aset of distance equations based at least in part on the set of timevalues and the set of distance expressions; and solving, by the one ormore computer processors, the set of distance equations to determine afirst position or a second position, wherein the first positionrepresents a position associated with the first vehicle within acoordinate system defined in relation to the one or more signal sources,and the second position represents a position associated with the one ormore signal sources within a coordinate system defined in relation tothe first vehicle.
 2. The method of claim 1 wherein the one or moresignal sensors comprise at least three signal sensors positioned on thefirst vehicle and the one or more signals comprise a signal received byeach of the at least three signal sensors from one signal source.
 3. Themethod of claim 1, wherein the one or more signals comprise at leastthree signals received from at least three respective correspondingsignal sources.
 4. The method of claim 1, wherein the set of time valuescomprises a difference in the arrival time, at the signal detectingunit, of each of the one or more signals in relation to the arrival timeof each of the other one or more signals, and each distance equationrepresents a difference between one distance expression and one otherdistance expression.
 5. The method of claim 1, further comprising:outputting, by the one or more computer processors, the first positionor the second position to at least one of a user interface or one ormore control units of the first vehicle.
 6. The method of claim 5,wherein the one or more control units are configured to control one ormore components of the first vehicle based at least in part on the firstposition or the second position.
 7. The method of claim 1, wherein theset of time values is determined based on phase differences among theone or more signals detected by the signal detecting unit.
 8. The methodof claim 1, wherein each of the one or more signals is a modulatedsignal that conveys information relating to a respective correspondingsignal source positioned on a second vehicle, the information comprisingat least one of an identifier associated with the second vehicle or aspatial coordinate associated with the respective corresponding signalsource.
 9. The method of claim 1, further comprising: solving, by theone or more computer processors, the set of distance equations todetermine a third position or a fourth position, wherein the thirdposition represents another position associated with the first vehiclewithin the coordinate system defined in relation to the one or moresignal sources, and the fourth position represents another positionassociated with the one or more signal sources within the coordinatesystem defined in relation to the first vehicle; and determining, by theone or more computer processors, an angular deviation between the firstvehicle and a second vehicle based at least in part on the first andthird positions or based at least in part on the second and fourthpositions.
 10. A system comprising: a signal detecting unit associatedwith a first vehicle, the signal detecting unit comprising one or moresignal sensors and one or more computer processors, wherein the signaldetecting unit is configured to detect one or more signals received fromone or more signal sources, and wherein the one or more processors areconfigured to: determine a set of time values based on arrival times ofthe one or more signals; generate a set of distance expressions, whereineach distance expression corresponds to a distance between one of theone or more signal sensors and one of the one or more signal sources;generate a set of distance equations based at least in part on the setof time values and the set of distance expressions; and solve the set ofdistance equations to determine a first position or a second position,wherein the first position represents a position associated with thefirst vehicle within a coordinate system defined in relation to the oneor more signal sources, and the second position represents a positionassociated with the one or more signal sources within a coordinatesystem defined in relation to the first vehicle.
 11. The system of claim10, wherein the one or more signal sensors comprise at least threesignal sensors positioned on the first vehicle and the one or moresignals comprise a signal received by each of the at least three signalsensors from one signal source.
 12. The system of claim 10, wherein theone or more signals comprise at least three signals received from atleast three respective corresponding signal sources.
 13. The system ofclaim 10, wherein the set of time values comprises a difference in thearrival time, at the signal detecting unit, of each of the one or moresignals in relation to the arrival time of each of the other one or moresignals, and each distance equation represents a difference between onedistance expression and one other distance expression.
 14. The system ofclaim 10, wherein the one or more computer processors are furtherconfigured to: output the first position or the second position to atleast one of a user interface or one or more control units of the firstvehicle.
 15. The system of claim 14, wherein the one or more controlunits are configured to control one or more components of the firstvehicle based on the first position or the second position.
 16. Thesystem of claim 10, wherein the set of time values is determined basedon phase differences among the one or more signals detected by thesignal detecting unit.
 17. The system of claim 10, wherein each of theone or more signals is a modulated signal that conveys informationrelating to a respective corresponding signal source positioned on asecond vehicle, the information comprising at least one of an identifierassociated with the second vehicle or a spatial coordinate associatedwith the respective corresponding signal source.
 18. The system of claim10, wherein the one or more computer processors are further configuredto: solve the set of distance equations to determine a third position ora fourth position, wherein the third position represents anotherposition associated with the first vehicle within the coordinate systemdefined in relation to the one or more signal sources, and the fourthposition represents another position associated with the one or moresignal sources within the coordinate system defined in relation to thefirst vehicle; and determine an angular deviation between the firstvehicle and a second vehicle based at least in part on the first andthird positions or based at least in part on the second and fourthpositions.
 19. One or more non-transitory computer-readable mediastoring computer-executable instructions that responsive to execution byone or more computer processors causes operations to be performedcomprising: detecting, at a signal detecting unit associated with afirst vehicle, one or more signals received from one or more signalsources; determining a set of time values based on arrival times of theone or more signals; generating a set of distance expressions, whereineach distance expression corresponds to a distance between one of theone or more signal sensors and one of the one or more signal sources;generating a set of distance equations based at least in part on the setof time values and the set of distance expressions; and solving the setof distance equations to determine a first position or a secondposition, wherein the first position represents a position associatedwith the first vehicle within a coordinate system defined in relation tothe one or more signal sources, and the second position represents aposition associated with the one or more signal sources within acoordinate system defined in relation to the first vehicle.
 20. The oneor more computer-readable media of claim 19, wherein the one or moresignal sensors comprise at least three signal sensors positioned on thefirst vehicle and the one or more signals comprise a signal received byeach of the at least three signal sensors from one signal source. 21.The one or more computer-readable media of claim 19, wherein the one ormore signals comprise at least three signals received from at leastthree respective corresponding signal sources.
 22. The one or morecomputer-readable media of claim 19, the operations further comprising:outputting the first position or the second position to at least one ofa user interface or one or more control units of the first vehicle. 23.The one or more computer-readable media of claim 19, the operationsfurther comprising: solving the set of distance equations to determine athird position or a fourth position, wherein the third positionrepresents another position associated with the first vehicle within thecoordinate system defined in relation to the one or more signal sources,and the fourth position represents another position associated with theone or more signal sources within the coordinate system defined inrelation to the first vehicle; and determining an angular deviationbetween the first vehicle and a second vehicle based at least in part onthe first and third positions or based at least in part on the secondand fourth positions.